A Generalized Convex Hull Construction for Computational Materials Discovery

Structure searches typically generate intractably large databases of locally-stable structures. Before determining accurate structural properties and synthesis pathways one must first identify those that can be synthesized (and are of practical interest).
Conventionally, structure searches use a convex hull construction to identify structures that (in the absence of kinetic effects) can be stabilized by manipulating a particular thermodynamic constraint chosen on the basis of experimental evidence or intuition. This is neither agnostic, nor capable of identifying structures stabilized by more complex sets of constraints.
We introduce a generalized convex hull (GCH) framework based on an abstract representation of structural similarity. The GCH is constructed on data-driven coordinates, which correspond to directions of maximum structural diversity, allowing us to single out structures that can be stabilized by general thermodynamic constraints, ranging from pressure to the substitution of portions of organic compounds.
Moreover, we rigorously account for the inevitable inaccuracies in the calculated structures data by sampling the resultant statistical distribution of GCHs. For each structure we thereby evaluate the probability that it can be stabilized.